//===- llvm/ADT/APFloat.h - Arbitrary Precision Floating Point ---*- C++ -*-==//
//
// The LLVM Compiler Infrastructure
//
// This file is distributed under the University of Illinois Open Source
// License. See LICENSE.TXT for details.
//
//===----------------------------------------------------------------------===//
///
/// \file
/// \brief
/// This file declares a class to represent arbitrary precision floating point
/// values and provide a variety of arithmetic operations on them.
///
//===----------------------------------------------------------------------===//
#ifndef LLVM_ADT_APFLOAT_H
#define LLVM_ADT_APFLOAT_H
#include "llvm/ADT/APInt.h"
#include "llvm/ADT/ArrayRef.h"
#include "llvm/Support/ErrorHandling.h"
#include <memory>
#define APFLOAT_DISPATCH_ON_SEMANTICS(METHOD_CALL) \
do { \
if (usesLayout<IEEEFloat>(getSemantics())) \
return U.IEEE.METHOD_CALL; \
if (usesLayout<DoubleAPFloat>(getSemantics())) \
return U.Double.METHOD_CALL; \
llvm_unreachable("Unexpected semantics"); \
} while (false)
namespace llvm {
struct fltSemantics;
class APSInt;
class StringRef;
class APFloat;
class raw_ostream;
template <typename T> class SmallVectorImpl;
/// Enum that represents what fraction of the LSB truncated bits of an fp number
/// represent.
///
/// This essentially combines the roles of guard and sticky bits.
enum lostFraction { // Example of truncated bits:
lfExactlyZero, // 000000
lfLessThanHalf, // 0xxxxx x's not all zero
lfExactlyHalf, // 100000
lfMoreThanHalf // 1xxxxx x's not all zero
};
/// A self-contained host- and target-independent arbitrary-precision
/// floating-point software implementation.
///
/// APFloat uses bignum integer arithmetic as provided by static functions in
/// the APInt class. The library will work with bignum integers whose parts are
/// any unsigned type at least 16 bits wide, but 64 bits is recommended.
///
/// Written for clarity rather than speed, in particular with a view to use in
/// the front-end of a cross compiler so that target arithmetic can be correctly
/// performed on the host. Performance should nonetheless be reasonable,
/// particularly for its intended use. It may be useful as a base
/// implementation for a run-time library during development of a faster
/// target-specific one.
///
/// All 5 rounding modes in the IEEE-754R draft are handled correctly for all
/// implemented operations. Currently implemented operations are add, subtract,
/// multiply, divide, fused-multiply-add, conversion-to-float,
/// conversion-to-integer and conversion-from-integer. New rounding modes
/// (e.g. away from zero) can be added with three or four lines of code.
///
/// Four formats are built-in: IEEE single precision, double precision,
/// quadruple precision, and x87 80-bit extended double (when operating with
/// full extended precision). Adding a new format that obeys IEEE semantics
/// only requires adding two lines of code: a declaration and definition of the
/// format.
///
/// All operations return the status of that operation as an exception bit-mask,
/// so multiple operations can be done consecutively with their results or-ed
/// together. The returned status can be useful for compiler diagnostics; e.g.,
/// inexact, underflow and overflow can be easily diagnosed on constant folding,
/// and compiler optimizers can determine what exceptions would be raised by
/// folding operations and optimize, or perhaps not optimize, accordingly.
///
/// At present, underflow tininess is detected after rounding; it should be
/// straight forward to add support for the before-rounding case too.
///
/// The library reads hexadecimal floating point numbers as per C99, and
/// correctly rounds if necessary according to the specified rounding mode.
/// Syntax is required to have been validated by the caller. It also converts
/// floating point numbers to hexadecimal text as per the C99 %a and %A
/// conversions. The output precision (or alternatively the natural minimal
/// precision) can be specified; if the requested precision is less than the
/// natural precision the output is correctly rounded for the specified rounding
/// mode.
///
/// It also reads decimal floating point numbers and correctly rounds according
/// to the specified rounding mode.
///
/// Conversion to decimal text is not currently implemented.
///
/// Non-zero finite numbers are represented internally as a sign bit, a 16-bit
/// signed exponent, and the significand as an array of integer parts. After
/// normalization of a number of precision P the exponent is within the range of
/// the format, and if the number is not denormal the P-th bit of the
/// significand is set as an explicit integer bit. For denormals the most
/// significant bit is shifted right so that the exponent is maintained at the
/// format's minimum, so that the smallest denormal has just the least
/// significant bit of the significand set. The sign of zeroes and infinities
/// is significant; the exponent and significand of such numbers is not stored,
/// but has a known implicit (deterministic) value: 0 for the significands, 0
/// for zero exponent, all 1 bits for infinity exponent. For NaNs the sign and
/// significand are deterministic, although not really meaningful, and preserved
/// in non-conversion operations. The exponent is implicitly all 1 bits.
///
/// APFloat does not provide any exception handling beyond default exception
/// handling. We represent Signaling NaNs via IEEE-754R 2008 6.2.1 should clause
/// by encoding Signaling NaNs with the first bit of its trailing significand as
/// 0.
///
/// TODO
/// ====
///
/// Some features that may or may not be worth adding:
///
/// Binary to decimal conversion (hard).
///
/// Optional ability to detect underflow tininess before rounding.
///
/// New formats: x87 in single and double precision mode (IEEE apart from
/// extended exponent range) (hard).
///
/// New operations: sqrt, IEEE remainder, C90 fmod, nexttoward.
///
// This is the common type definitions shared by APFloat and its internal
// implementation classes. This struct should not define any non-static data
// members.
struct APFloatBase {
typedef APInt::WordType integerPart;
static const unsigned integerPartWidth = APInt::APINT_BITS_PER_WORD;
/// A signed type to represent a floating point numbers unbiased exponent.
typedef signed short ExponentType;
/// \name Floating Point Semantics.
/// @{
static const fltSemantics &IEEEhalf() LLVM_READNONE;
static const fltSemantics &IEEEsingle() LLVM_READNONE;
static const fltSemantics &IEEEdouble() LLVM_READNONE;
static const fltSemantics &IEEEquad() LLVM_READNONE;
static const fltSemantics &PPCDoubleDouble() LLVM_READNONE;
static const fltSemantics &x87DoubleExtended() LLVM_READNONE;
/// A Pseudo fltsemantic used to construct APFloats that cannot conflict with
/// anything real.
static const fltSemantics &Bogus() LLVM_READNONE;
/// @}
/// IEEE-754R 5.11: Floating Point Comparison Relations.
enum cmpResult {
cmpLessThan,
cmpEqual,
cmpGreaterThan,
cmpUnordered
};
/// IEEE-754R 4.3: Rounding-direction attributes.
enum roundingMode {
rmNearestTiesToEven,
rmTowardPositive,
rmTowardNegative,
rmTowardZero,
rmNearestTiesToAway
};
/// IEEE-754R 7: Default exception handling.
///
/// opUnderflow or opOverflow are always returned or-ed with opInexact.
enum opStatus {
opOK = 0x00,
opInvalidOp = 0x01,
opDivByZero = 0x02,
opOverflow = 0x04,
opUnderflow = 0x08,
opInexact = 0x10
};
/// Category of internally-represented number.
enum fltCategory {
fcInfinity,
fcNaN,
fcNormal,
fcZero
};
/// Convenience enum used to construct an uninitialized APFloat.
enum uninitializedTag {
uninitialized
};
/// Enumeration of \c ilogb error results.
enum IlogbErrorKinds {
IEK_Zero = INT_MIN + 1,
IEK_NaN = INT_MIN,
IEK_Inf = INT_MAX
};
static unsigned int semanticsPrecision(const fltSemantics &);
static ExponentType semanticsMinExponent(const fltSemantics &);
static ExponentType semanticsMaxExponent(const fltSemantics &);
static unsigned int semanticsSizeInBits(const fltSemantics &);
/// Returns the size of the floating point number (in bits) in the given
/// semantics.
static unsigned getSizeInBits(const fltSemantics &Sem);
};
namespace detail {
class IEEEFloat final : public APFloatBase {
public:
/// \name Constructors
/// @{
IEEEFloat(const fltSemantics &); // Default construct to 0.0
IEEEFloat(const fltSemantics &, integerPart);
IEEEFloat(const fltSemantics &, uninitializedTag);
IEEEFloat(const fltSemantics &, const APInt &);
explicit IEEEFloat(double d);
explicit IEEEFloat(float f);
IEEEFloat(const IEEEFloat &);
IEEEFloat(IEEEFloat &&);
~IEEEFloat();
/// @}
/// Returns whether this instance allocated memory.
bool needsCleanup() const { return partCount() > 1; }
/// \name Convenience "constructors"
/// @{
/// @}
/// \name Arithmetic
/// @{
opStatus add(const IEEEFloat &, roundingMode);
opStatus subtract(const IEEEFloat &, roundingMode);
opStatus multiply(const IEEEFloat &, roundingMode);
opStatus divide(const IEEEFloat &, roundingMode);
/// IEEE remainder.
opStatus remainder(const IEEEFloat &);
/// C fmod, or llvm frem.
opStatus mod(const IEEEFloat &);
opStatus fusedMultiplyAdd(const IEEEFloat &, const IEEEFloat &, roundingMode);
opStatus roundToIntegral(roundingMode);
/// IEEE-754R 5.3.1: nextUp/nextDown.
opStatus next(bool nextDown);
/// @}
/// \name Sign operations.
/// @{
void changeSign();
/// @}
/// \name Conversions
/// @{
opStatus convert(const fltSemantics &, roundingMode, bool *);
opStatus convertToInteger(MutableArrayRef<integerPart>, unsigned int, bool,
roundingMode, bool *) const;
opStatus convertFromAPInt(const APInt &, bool, roundingMode);
opStatus convertFromSignExtendedInteger(const integerPart *, unsigned int,
bool, roundingMode);
opStatus convertFromZeroExtendedInteger(const integerPart *, unsigned int,
bool, roundingMode);
opStatus convertFromString(StringRef, roundingMode);
APInt bitcastToAPInt() const;
double convertToDouble() const;
float convertToFloat() const;
/// @}
/// The definition of equality is not straightforward for floating point, so
/// we won't use operator==. Use one of the following, or write whatever it
/// is you really mean.
bool operator==(const IEEEFloat &) const = delete;
/// IEEE comparison with another floating point number (NaNs compare
/// unordered, 0==-0).
cmpResult compare(const IEEEFloat &) const;
/// Bitwise comparison for equality (QNaNs compare equal, 0!=-0).
bool bitwiseIsEqual(const IEEEFloat &) const;
/// Write out a hexadecimal representation of the floating point value to DST,
/// which must be of sufficient size, in the C99 form [-]0xh.hhhhp[+-]d.
/// Return the number of characters written, excluding the terminating NUL.
unsigned int convertToHexString(char *dst, unsigned int hexDigits,
bool upperCase, roundingMode) const;
/// \name IEEE-754R 5.7.2 General operations.
/// @{
/// IEEE-754R isSignMinus: Returns true if and only if the current value is
/// negative.
///
/// This applies to zeros and NaNs as well.
bool isNegative() const { return sign; }
/// IEEE-754R isNormal: Returns true if and only if the current value is normal.
///
/// This implies that the current value of the float is not zero, subnormal,
/// infinite, or NaN following the definition of normality from IEEE-754R.
bool isNormal() const { return !isDenormal() && isFiniteNonZero(); }
/// Returns true if and only if the current value is zero, subnormal, or
/// normal.
///
/// This means that the value is not infinite or NaN.
bool isFinite() const { return !isNaN() && !isInfinity(); }
/// Returns true if and only if the float is plus or minus zero.
bool isZero() const { return category == fcZero; }
/// IEEE-754R isSubnormal(): Returns true if and only if the float is a
/// denormal.
bool isDenormal() const;
/// IEEE-754R isInfinite(): Returns true if and only if the float is infinity.
bool isInfinity() const { return category == fcInfinity; }
/// Returns true if and only if the float is a quiet or signaling NaN.
bool isNaN() const { return category == fcNaN; }
/// Returns true if and only if the float is a signaling NaN.
bool isSignaling() const;
/// @}
/// \name Simple Queries
/// @{
fltCategory getCategory() const { return category; }
const fltSemantics &getSemantics() const { return *semantics; }
bool isNonZero() const { return category != fcZero; }
bool isFiniteNonZero() const { return isFinite() && !isZero(); }
bool isPosZero() const { return isZero() && !isNegative(); }
bool isNegZero() const { return isZero() && isNegative(); }
/// Returns true if and only if the number has the smallest possible non-zero
/// magnitude in the current semantics.
bool isSmallest() const;
/// Returns true if and only if the number has the largest possible finite
/// magnitude in the current semantics.
bool isLargest() const;
/// Returns true if and only if the number is an exact integer.
bool isInteger() const;
/// @}
IEEEFloat &operator=(const IEEEFloat &);
IEEEFloat &operator=(IEEEFloat &&);
/// Overload to compute a hash code for an APFloat value.
///
/// Note that the use of hash codes for floating point values is in general
/// frought with peril. Equality is hard to define for these values. For
/// example, should negative and positive zero hash to different codes? Are
/// they equal or not? This hash value implementation specifically
/// emphasizes producing different codes for different inputs in order to
/// be used in canonicalization and memoization. As such, equality is
/// bitwiseIsEqual, and 0 != -0.
friend hash_code hash_value(const IEEEFloat &Arg);
/// Converts this value into a decimal string.
///
/// \param FormatPrecision The maximum number of digits of
/// precision to output. If there are fewer digits available,
/// zero padding will not be used unless the value is
/// integral and small enough to be expressed in
/// FormatPrecision digits. 0 means to use the natural
/// precision of the number.
/// \param FormatMaxPadding The maximum number of zeros to
/// consider inserting before falling back to scientific
/// notation. 0 means to always use scientific notation.
///
/// \param TruncateZero Indicate whether to remove the trailing zero in
/// fraction part or not. Also setting this parameter to false forcing
/// producing of output more similar to default printf behavior.
/// Specifically the lower e is used as exponent delimiter and exponent
/// always contains no less than two digits.
///
/// Number Precision MaxPadding Result
/// ------ --------- ---------- ------
/// 1.01E+4 5 2 10100
/// 1.01E+4 4 2 1.01E+4
/// 1.01E+4 5 1 1.01E+4
/// 1.01E-2 5 2 0.0101
/// 1.01E-2 4 2 0.0101
/// 1.01E-2 4 1 1.01E-2
void toString(SmallVectorImpl<char> &Str, unsigned FormatPrecision = 0,
unsigned FormatMaxPadding = 3, bool TruncateZero = true) const;
/// If this value has an exact multiplicative inverse, store it in inv and
/// return true.
bool getExactInverse(APFloat *inv) const;
/// Returns the exponent of the internal representation of the APFloat.
///
/// Because the radix of APFloat is 2, this is equivalent to floor(log2(x)).
/// For special APFloat values, this returns special error codes:
///
/// NaN -> \c IEK_NaN
/// 0 -> \c IEK_Zero
/// Inf -> \c IEK_Inf
///
friend int ilogb(const IEEEFloat &Arg);
/// Returns: X * 2^Exp for integral exponents.
friend IEEEFloat scalbn(IEEEFloat X, int Exp, roundingMode);
friend IEEEFloat frexp(const IEEEFloat &X, int &Exp, roundingMode);
/// \name Special value setters.
/// @{
void makeLargest(bool Neg = false);
void makeSmallest(bool Neg = false);
void makeNaN(bool SNaN = false, bool Neg = false,
const APInt *fill = nullptr);
void makeInf(bool Neg = false);
void makeZero(bool Neg = false);
void makeQuiet();
/// Returns the smallest (by magnitude) normalized finite number in the given
/// semantics.
///
/// \param Negative - True iff the number should be negative
void makeSmallestNormalized(bool Negative = false);
/// @}
cmpResult compareAbsoluteValue(const IEEEFloat &) const;
private:
/// \name Simple Queries
/// @{
integerPart *significandParts();
const integerPart *significandParts() const;
unsigned int partCount() const;
/// @}
/// \name Significand operations.
/// @{
integerPart addSignificand(const IEEEFloat &);
integerPart subtractSignificand(const IEEEFloat &, integerPart);
lostFraction addOrSubtractSignificand(const IEEEFloat &, bool subtract);
lostFraction multiplySignificand(const IEEEFloat &, const IEEEFloat *);
lostFraction divideSignificand(const IEEEFloat &);
void incrementSignificand();
void initialize(const fltSemantics *);
void shiftSignificandLeft(unsigned int);
lostFraction shiftSignificandRight(unsigned int);
unsigned int significandLSB() const;
unsigned int significandMSB() const;
void zeroSignificand();
/// Return true if the significand excluding the integral bit is all ones.
bool isSignificandAllOnes() const;
/// Return true if the significand excluding the integral bit is all zeros.
bool isSignificandAllZeros() const;
/// @}
/// \name Arithmetic on special values.
/// @{
opStatus addOrSubtractSpecials(const IEEEFloat &, bool subtract);
opStatus divideSpecials(const IEEEFloat &);
opStatus multiplySpecials(const IEEEFloat &);
opStatus modSpecials(const IEEEFloat &);
/// @}
/// \name Miscellany
/// @{
bool convertFromStringSpecials(StringRef str);
opStatus normalize(roundingMode, lostFraction);
opStatus addOrSubtract(const IEEEFloat &, roundingMode, bool subtract);
opStatus handleOverflow(roundingMode);
bool roundAwayFromZero(roundingMode, lostFraction, unsigned int) const;
opStatus convertToSignExtendedInteger(MutableArrayRef<integerPart>,
unsigned int, bool, roundingMode,
bool *) const;
opStatus convertFromUnsignedParts(const integerPart *, unsigned int,
roundingMode);
opStatus convertFromHexadecimalString(StringRef, roundingMode);
opStatus convertFromDecimalString(StringRef, roundingMode);
char *convertNormalToHexString(char *, unsigned int, bool,
roundingMode) const;
opStatus roundSignificandWithExponent(const integerPart *, unsigned int, int,
roundingMode);
/// @}
APInt convertHalfAPFloatToAPInt() const;
APInt convertFloatAPFloatToAPInt() const;
APInt convertDoubleAPFloatToAPInt() const;
APInt convertQuadrupleAPFloatToAPInt() const;
APInt convertF80LongDoubleAPFloatToAPInt() const;
APInt convertPPCDoubleDoubleAPFloatToAPInt() const;
void initFromAPInt(const fltSemantics *Sem, const APInt &api);
void initFromHalfAPInt(const APInt &api);
void initFromFloatAPInt(const APInt &api);
void initFromDoubleAPInt(const APInt &api);
void initFromQuadrupleAPInt(const APInt &api);
void initFromF80LongDoubleAPInt(const APInt &api);
void initFromPPCDoubleDoubleAPInt(const APInt &api);
void assign(const IEEEFloat &);
void copySignificand(const IEEEFloat &);
void freeSignificand();
/// Note: this must be the first data member.
/// The semantics that this value obeys.
const fltSemantics *semantics;
/// A binary fraction with an explicit integer bit.
///
/// The significand must be at least one bit wider than the target precision.
union Significand {
integerPart part;
integerPart *parts;
} significand;
/// The signed unbiased exponent of the value.
ExponentType exponent;
/// What kind of floating point number this is.
///
/// Only 2 bits are required, but VisualStudio incorrectly sign extends it.
/// Using the extra bit keeps it from failing under VisualStudio.
fltCategory category : 3;
/// Sign bit of the number.
unsigned int sign : 1;
};
hash_code hash_value(const IEEEFloat &Arg);
int ilogb(const IEEEFloat &Arg);
IEEEFloat scalbn(IEEEFloat X, int Exp, IEEEFloat::roundingMode);
IEEEFloat frexp(const IEEEFloat &Val, int &Exp, IEEEFloat::roundingMode RM);
// This mode implements more precise float in terms of two APFloats.
// The interface and layout is designed for arbitray underlying semantics,
// though currently only PPCDoubleDouble semantics are supported, whose
// corresponding underlying semantics are IEEEdouble.
class DoubleAPFloat final : public APFloatBase {
// Note: this must be the first data member.
const fltSemantics *Semantics;
std::unique_ptr<APFloat[]> Floats;
opStatus addImpl(const APFloat &a, const APFloat &aa, const APFloat &c,
const APFloat &cc, roundingMode RM);
opStatus addWithSpecial(const DoubleAPFloat &LHS, const DoubleAPFloat &RHS,
DoubleAPFloat &Out, roundingMode RM);
public:
DoubleAPFloat(const fltSemantics &S);
DoubleAPFloat(const fltSemantics &S, uninitializedTag);
DoubleAPFloat(const fltSemantics &S, integerPart);
DoubleAPFloat(const fltSemantics &S, const APInt &I);
DoubleAPFloat(const fltSemantics &S, APFloat &&First, APFloat &&Second);
DoubleAPFloat(const DoubleAPFloat &RHS);
DoubleAPFloat(DoubleAPFloat &&RHS);
DoubleAPFloat &operator=(const DoubleAPFloat &RHS);
DoubleAPFloat &operator=(DoubleAPFloat &&RHS) {
if (this != &RHS) {
this->~DoubleAPFloat();
new (this) DoubleAPFloat(std::move(RHS));
}
return *this;
}
bool needsCleanup() const { return Floats != nullptr; }
APFloat &getFirst() { return Floats[0]; }
const APFloat &getFirst() const { return Floats[0]; }
APFloat &getSecond() { return Floats[1]; }
const APFloat &getSecond() const { return Floats[1]; }
opStatus add(const DoubleAPFloat &RHS, roundingMode RM);
opStatus subtract(const DoubleAPFloat &RHS, roundingMode RM);
opStatus multiply(const DoubleAPFloat &RHS, roundingMode RM);
opStatus divide(const DoubleAPFloat &RHS, roundingMode RM);
opStatus remainder(const DoubleAPFloat &RHS);
opStatus mod(const DoubleAPFloat &RHS);
opStatus fusedMultiplyAdd(const DoubleAPFloat &Multiplicand,
const DoubleAPFloat &Addend, roundingMode RM);
opStatus roundToIntegral(roundingMode RM);
void changeSign();
cmpResult compareAbsoluteValue(const DoubleAPFloat &RHS) const;
fltCategory getCategory() const;
bool isNegative() const;
void makeInf(bool Neg);
void makeZero(bool Neg);
void makeLargest(bool Neg);
void makeSmallest(bool Neg);
void makeSmallestNormalized(bool Neg);
void makeNaN(bool SNaN, bool Neg, const APInt *fill);
cmpResult compare(const DoubleAPFloat &RHS) const;
bool bitwiseIsEqual(const DoubleAPFloat &RHS) const;
APInt bitcastToAPInt() const;
opStatus convertFromString(StringRef, roundingMode);
opStatus next(bool nextDown);
opStatus convertToInteger(MutableArrayRef<integerPart> Input,
unsigned int Width, bool IsSigned, roundingMode RM,
bool *IsExact) const;
opStatus convertFromAPInt(const APInt &Input, bool IsSigned, roundingMode RM);
opStatus convertFromSignExtendedInteger(const integerPart *Input,
unsigned int InputSize, bool IsSigned,
roundingMode RM);
opStatus convertFromZeroExtendedInteger(const integerPart *Input,
unsigned int InputSize, bool IsSigned,
roundingMode RM);
unsigned int convertToHexString(char *DST, unsigned int HexDigits,
bool UpperCase, roundingMode RM) const;
bool isDenormal() const;
bool isSmallest() const;
bool isLargest() const;
bool isInteger() const;
void toString(SmallVectorImpl<char> &Str, unsigned FormatPrecision,
unsigned FormatMaxPadding, bool TruncateZero = true) const;
bool getExactInverse(APFloat *inv) const;
friend int ilogb(const DoubleAPFloat &Arg);
friend DoubleAPFloat scalbn(DoubleAPFloat X, int Exp, roundingMode);
friend DoubleAPFloat frexp(const DoubleAPFloat &X, int &Exp, roundingMode);
friend hash_code hash_value(const DoubleAPFloat &Arg);
};
hash_code hash_value(const DoubleAPFloat &Arg);
} // End detail namespace
// This is a interface class that is currently forwarding functionalities from
// detail::IEEEFloat.
class APFloat : public APFloatBase {
typedef detail::IEEEFloat IEEEFloat;
typedef detail::DoubleAPFloat DoubleAPFloat;
static_assert(std::is_standard_layout<IEEEFloat>::value, "");
union Storage {
const fltSemantics *semantics;
IEEEFloat IEEE;
DoubleAPFloat Double;
explicit Storage(IEEEFloat F, const fltSemantics &S);
explicit Storage(DoubleAPFloat F, const fltSemantics &S)
: Double(std::move(F)) {
assert(&S == &PPCDoubleDouble());
}
template <typename... ArgTypes>
Storage(const fltSemantics &Semantics, ArgTypes &&... Args) {
if (usesLayout<IEEEFloat>(Semantics)) {
new (&IEEE) IEEEFloat(Semantics, std::forward<ArgTypes>(Args)...);
return;
}
if (usesLayout<DoubleAPFloat>(Semantics)) {
new (&Double) DoubleAPFloat(Semantics, std::forward<ArgTypes>(Args)...);
return;
}
llvm_unreachable("Unexpected semantics");
}
~Storage() {
if (usesLayout<IEEEFloat>(*semantics)) {
IEEE.~IEEEFloat();
return;
}
if (usesLayout<DoubleAPFloat>(*semantics)) {
Double.~DoubleAPFloat();
return;
}
llvm_unreachable("Unexpected semantics");
}
Storage(const Storage &RHS) {
if (usesLayout<IEEEFloat>(*RHS.semantics)) {
new (this) IEEEFloat(RHS.IEEE);
return;
}
if (usesLayout<DoubleAPFloat>(*RHS.semantics)) {
new (this) DoubleAPFloat(RHS.Double);
return;
}
llvm_unreachable("Unexpected semantics");
}
Storage(Storage &&RHS) {
if (usesLayout<IEEEFloat>(*RHS.semantics)) {
new (this) IEEEFloat(std::move(RHS.IEEE));
return;
}
if (usesLayout<DoubleAPFloat>(*RHS.semantics)) {
new (this) DoubleAPFloat(std::move(RHS.Double));
return;
}
llvm_unreachable("Unexpected semantics");
}
Storage &operator=(const Storage &RHS) {
if (usesLayout<IEEEFloat>(*semantics) &&
usesLayout<IEEEFloat>(*RHS.semantics)) {
IEEE = RHS.IEEE;
} else if (usesLayout<DoubleAPFloat>(*semantics) &&
usesLayout<DoubleAPFloat>(*RHS.semantics)) {
Double = RHS.Double;
} else if (this != &RHS) {
this->~Storage();
new (this) Storage(RHS);
}
return *this;
}
Storage &operator=(Storage &&RHS) {
if (usesLayout<IEEEFloat>(*semantics) &&
usesLayout<IEEEFloat>(*RHS.semantics)) {
IEEE = std::move(RHS.IEEE);
} else if (usesLayout<DoubleAPFloat>(*semantics) &&
usesLayout<DoubleAPFloat>(*RHS.semantics)) {
Double = std::move(RHS.Double);
} else if (this != &RHS) {
this->~Storage();
new (this) Storage(std::move(RHS));
}
return *this;
}
} U;
template <typename T> static bool usesLayout(const fltSemantics &Semantics) {
static_assert(std::is_same<T, IEEEFloat>::value ||
std::is_same<T, DoubleAPFloat>::value, "");
if (std::is_same<T, DoubleAPFloat>::value) {
return &Semantics == &PPCDoubleDouble();
}
return &Semantics != &PPCDoubleDouble();
}
IEEEFloat &getIEEE() {
if (usesLayout<IEEEFloat>(*U.semantics))
return U.IEEE;
if (usesLayout<DoubleAPFloat>(*U.semantics))
return U.Double.getFirst().U.IEEE;
llvm_unreachable("Unexpected semantics");
}
const IEEEFloat &getIEEE() const {
if (usesLayout<IEEEFloat>(*U.semantics))
return U.IEEE;
if (usesLayout<DoubleAPFloat>(*U.semantics))
return U.Double.getFirst().U.IEEE;
llvm_unreachable("Unexpected semantics");
}
void makeZero(bool Neg) { APFLOAT_DISPATCH_ON_SEMANTICS(makeZero(Neg)); }
void makeInf(bool Neg) { APFLOAT_DISPATCH_ON_SEMANTICS(makeInf(Neg)); }
void makeNaN(bool SNaN, bool Neg, const APInt *fill) {
APFLOAT_DISPATCH_ON_SEMANTICS(makeNaN(SNaN, Neg, fill));
}
void makeLargest(bool Neg) {
APFLOAT_DISPATCH_ON_SEMANTICS(makeLargest(Neg));
}
void makeSmallest(bool Neg) {
APFLOAT_DISPATCH_ON_SEMANTICS(makeSmallest(Neg));
}
void makeSmallestNormalized(bool Neg) {
APFLOAT_DISPATCH_ON_SEMANTICS(makeSmallestNormalized(Neg));
}
// FIXME: This is due to clang 3.3 (or older version) always checks for the
// default constructor in an array aggregate initialization, even if no
// elements in the array is default initialized.
APFloat() : U(IEEEdouble()) {
llvm_unreachable("This is a workaround for old clang.");
}
explicit APFloat(IEEEFloat F, const fltSemantics &S) : U(std::move(F), S) {}
explicit APFloat(DoubleAPFloat F, const fltSemantics &S)
: U(std::move(F), S) {}
cmpResult compareAbsoluteValue(const APFloat &RHS) const {
assert(&getSemantics() == &RHS.getSemantics() &&
"Should only compare APFloats with the same semantics");
if (usesLayout<IEEEFloat>(getSemantics()))
return U.IEEE.compareAbsoluteValue(RHS.U.IEEE);
if (usesLayout<DoubleAPFloat>(getSemantics()))
return U.Double.compareAbsoluteValue(RHS.U.Double);
llvm_unreachable("Unexpected semantics");
}
public:
APFloat(const fltSemantics &Semantics) : U(Semantics) {}
APFloat(const fltSemantics &Semantics, StringRef S);
APFloat(const fltSemantics &Semantics, integerPart I) : U(Semantics, I) {}
// TODO: Remove this constructor. This isn't faster than the first one.
APFloat(const fltSemantics &Semantics, uninitializedTag)
: U(Semantics, uninitialized) {}
APFloat(const fltSemantics &Semantics, const APInt &I) : U(Semantics, I) {}
explicit APFloat(double d) : U(IEEEFloat(d), IEEEdouble()) {}
explicit APFloat(float f) : U(IEEEFloat(f), IEEEsingle()) {}
APFloat(const APFloat &RHS) = default;
APFloat(APFloat &&RHS) = default;
~APFloat() = default;
bool needsCleanup() const { APFLOAT_DISPATCH_ON_SEMANTICS(needsCleanup()); }
/// Factory for Positive and Negative Zero.
///
/// \param Negative True iff the number should be negative.
static APFloat getZero(const fltSemantics &Sem, bool Negative = false) {
APFloat Val(Sem, uninitialized);
Val.makeZero(Negative);
return Val;
}
/// Factory for Positive and Negative Infinity.
///
/// \param Negative True iff the number should be negative.
static APFloat getInf(const fltSemantics &Sem, bool Negative = false) {
APFloat Val(Sem, uninitialized);
Val.makeInf(Negative);
return Val;
}
/// Factory for NaN values.
///
/// \param Negative - True iff the NaN generated should be negative.
/// \param payload - The unspecified fill bits for creating the NaN, 0 by
/// default. The value is truncated as necessary.
static APFloat getNaN(const fltSemantics &Sem, bool Negative = false,
uint64_t payload = 0) {
if (payload) {
APInt intPayload(64, payload);
return getQNaN(Sem, Negative, &intPayload);
} else {
return getQNaN(Sem, Negative, nullptr);
}
}
/// Factory for QNaN values.
static APFloat getQNaN(const fltSemantics &Sem, bool Negative = false,
const APInt *payload = nullptr) {
APFloat Val(Sem, uninitialized);
Val.makeNaN(false, Negative, payload);
return Val;
}
/// Factory for SNaN values.
static APFloat getSNaN(const fltSemantics &Sem, bool Negative = false,
const APInt *payload = nullptr) {
APFloat Val(Sem, uninitialized);
Val.makeNaN(true, Negative, payload);
return Val;
}
/// Returns the largest finite number in the given semantics.
///
/// \param Negative - True iff the number should be negative
static APFloat getLargest(const fltSemantics &Sem, bool Negative = false) {
APFloat Val(Sem, uninitialized);
Val.makeLargest(Negative);
return Val;
}
/// Returns the smallest (by magnitude) finite number in the given semantics.
/// Might be denormalized, which implies a relative loss of precision.
///
/// \param Negative - True iff the number should be negative
static APFloat getSmallest(const fltSemantics &Sem, bool Negative = false) {
APFloat Val(Sem, uninitialized);
Val.makeSmallest(Negative);
return Val;
}
/// Returns the smallest (by magnitude) normalized finite number in the given
/// semantics.
///
/// \param Negative - True iff the number should be negative
static APFloat getSmallestNormalized(const fltSemantics &Sem,
bool Negative = false) {
APFloat Val(Sem, uninitialized);
Val.makeSmallestNormalized(Negative);
return Val;
}
/// Returns a float which is bitcasted from an all one value int.
///
/// \param BitWidth - Select float type
/// \param isIEEE - If 128 bit number, select between PPC and IEEE
static APFloat getAllOnesValue(unsigned BitWidth, bool isIEEE = false);
/// Used to insert APFloat objects, or objects that contain APFloat objects,
/// into FoldingSets.
void Profile(FoldingSetNodeID &NID) const;
opStatus add(const APFloat &RHS, roundingMode RM) {
assert(&getSemantics() == &RHS.getSemantics() &&
"Should only call on two APFloats with the same semantics");
if (usesLayout<IEEEFloat>(getSemantics()))
return U.IEEE.add(RHS.U.IEEE, RM);
if (usesLayout<DoubleAPFloat>(getSemantics()))
return U.Double.add(RHS.U.Double, RM);
llvm_unreachable("Unexpected semantics");
}
opStatus subtract(const APFloat &RHS, roundingMode RM) {
assert(&getSemantics() == &RHS.getSemantics() &&
"Should only call on two APFloats with the same semantics");
if (usesLayout<IEEEFloat>(getSemantics()))
return U.IEEE.subtract(RHS.U.IEEE, RM);
if (usesLayout<DoubleAPFloat>(getSemantics()))
return U.Double.subtract(RHS.U.Double, RM);
llvm_unreachable("Unexpected semantics");
}
opStatus multiply(const APFloat &RHS, roundingMode RM) {
assert(&getSemantics() == &RHS.getSemantics() &&
"Should only call on two APFloats with the same semantics");
if (usesLayout<IEEEFloat>(getSemantics()))
return U.IEEE.multiply(RHS.U.IEEE, RM);
if (usesLayout<DoubleAPFloat>(getSemantics()))
return U.Double.multiply(RHS.U.Double, RM);
llvm_unreachable("Unexpected semantics");
}
opStatus divide(const APFloat &RHS, roundingMode RM) {
assert(&getSemantics() == &RHS.getSemantics() &&
"Should only call on two APFloats with the same semantics");
if (usesLayout<IEEEFloat>(getSemantics()))
return U.IEEE.divide(RHS.U.IEEE, RM);
if (usesLayout<DoubleAPFloat>(getSemantics()))
return U.Double.divide(RHS.U.Double, RM);
llvm_unreachable("Unexpected semantics");
}
opStatus remainder(const APFloat &RHS) {
assert(&getSemantics() == &RHS.getSemantics() &&
"Should only call on two APFloats with the same semantics");
if (usesLayout<IEEEFloat>(getSemantics()))
return U.IEEE.remainder(RHS.U.IEEE);
if (usesLayout<DoubleAPFloat>(getSemantics()))
return U.Double.remainder(RHS.U.Double);
llvm_unreachable("Unexpected semantics");
}
opStatus mod(const APFloat &RHS) {
assert(&getSemantics() == &RHS.getSemantics() &&
"Should only call on two APFloats with the same semantics");
if (usesLayout<IEEEFloat>(getSemantics()))
return U.IEEE.mod(RHS.U.IEEE);
if (usesLayout<DoubleAPFloat>(getSemantics()))
return U.Double.mod(RHS.U.Double);
llvm_unreachable("Unexpected semantics");
}
opStatus fusedMultiplyAdd(const APFloat &Multiplicand, const APFloat &Addend,
roundingMode RM) {
assert(&getSemantics() == &Multiplicand.getSemantics() &&
"Should only call on APFloats with the same semantics");
assert(&getSemantics() == &Addend.getSemantics() &&
"Should only call on APFloats with the same semantics");
if (usesLayout<IEEEFloat>(getSemantics()))
return U.IEEE.fusedMultiplyAdd(Multiplicand.U.IEEE, Addend.U.IEEE, RM);
if (usesLayout<DoubleAPFloat>(getSemantics()))
return U.Double.fusedMultiplyAdd(Multiplicand.U.Double, Addend.U.Double,
RM);
llvm_unreachable("Unexpected semantics");
}
opStatus roundToIntegral(roundingMode RM) {
APFLOAT_DISPATCH_ON_SEMANTICS(roundToIntegral(RM));
}
// TODO: bool parameters are not readable and a source of bugs.
// Do something.
opStatus next(bool nextDown) {
APFLOAT_DISPATCH_ON_SEMANTICS(next(nextDown));
}
/// Add two APFloats, rounding ties to the nearest even.
/// No error checking.
APFloat operator+(const APFloat &RHS) const {
APFloat Result(*this);
(void)Result.add(RHS, rmNearestTiesToEven);
return Result;
}
/// Subtract two APFloats, rounding ties to the nearest even.
/// No error checking.
APFloat operator-(const APFloat &RHS) const {
APFloat Result(*this);
(void)Result.subtract(RHS, rmNearestTiesToEven);
return Result;
}
/// Multiply two APFloats, rounding ties to the nearest even.
/// No error checking.
APFloat operator*(const APFloat &RHS) const {
APFloat Result(*this);
(void)Result.multiply(RHS, rmNearestTiesToEven);
return Result;
}
/// Divide the first APFloat by the second, rounding ties to the nearest even.
/// No error checking.
APFloat operator/(const APFloat &RHS) const {
APFloat Result(*this);
(void)Result.divide(RHS, rmNearestTiesToEven);
return Result;
}
void changeSign() { APFLOAT_DISPATCH_ON_SEMANTICS(changeSign()); }
void clearSign() {
if (isNegative())
changeSign();
}
void copySign(const APFloat &RHS) {
if (isNegative() != RHS.isNegative())
changeSign();
}
/// A static helper to produce a copy of an APFloat value with its sign
/// copied from some other APFloat.
static APFloat copySign(APFloat Value, const APFloat &Sign) {
Value.copySign(Sign);
return Value;
}
opStatus convert(const fltSemantics &ToSemantics, roundingMode RM,
bool *losesInfo);
opStatus convertToInteger(MutableArrayRef<integerPart> Input,
unsigned int Width, bool IsSigned, roundingMode RM,
bool *IsExact) const {
APFLOAT_DISPATCH_ON_SEMANTICS(
convertToInteger(Input, Width, IsSigned, RM, IsExact));
}
opStatus convertToInteger(APSInt &Result, roundingMode RM,
bool *IsExact) const;
opStatus convertFromAPInt(const APInt &Input, bool IsSigned,
roundingMode RM) {
APFLOAT_DISPATCH_ON_SEMANTICS(convertFromAPInt(Input, IsSigned, RM));
}
opStatus convertFromSignExtendedInteger(const integerPart *Input,
unsigned int InputSize, bool IsSigned,
roundingMode RM) {
APFLOAT_DISPATCH_ON_SEMANTICS(
convertFromSignExtendedInteger(Input, InputSize, IsSigned, RM));
}
opStatus convertFromZeroExtendedInteger(const integerPart *Input,
unsigned int InputSize, bool IsSigned,
roundingMode RM) {
APFLOAT_DISPATCH_ON_SEMANTICS(
convertFromZeroExtendedInteger(Input, InputSize, IsSigned, RM));
}
opStatus convertFromString(StringRef, roundingMode);
APInt bitcastToAPInt() const {
APFLOAT_DISPATCH_ON_SEMANTICS(bitcastToAPInt());
}
double convertToDouble() const { return getIEEE().convertToDouble(); }
float convertToFloat() const { return getIEEE().convertToFloat(); }
bool operator==(const APFloat &) const = delete;
cmpResult compare(const APFloat &RHS) const {
assert(&getSemantics() == &RHS.getSemantics() &&
"Should only compare APFloats with the same semantics");
if (usesLayout<IEEEFloat>(getSemantics()))
return U.IEEE.compare(RHS.U.IEEE);
if (usesLayout<DoubleAPFloat>(getSemantics()))
return U.Double.compare(RHS.U.Double);
llvm_unreachable("Unexpected semantics");
}
bool bitwiseIsEqual(const APFloat &RHS) const {
if (&getSemantics() != &RHS.getSemantics())
return false;
if (usesLayout<IEEEFloat>(getSemantics()))
return U.IEEE.bitwiseIsEqual(RHS.U.IEEE);
if (usesLayout<DoubleAPFloat>(getSemantics()))
return U.Double.bitwiseIsEqual(RHS.U.Double);
llvm_unreachable("Unexpected semantics");
}
/// We don't rely on operator== working on double values, as
/// it returns true for things that are clearly not equal, like -0.0 and 0.0.
/// As such, this method can be used to do an exact bit-for-bit comparison of
/// two floating point values.
///
/// We leave the version with the double argument here because it's just so
/// convenient to write "2.0" and the like. Without this function we'd
/// have to duplicate its logic everywhere it's called.
bool isExactlyValue(double V) const {
bool ignored;
APFloat Tmp(V);
Tmp.convert(getSemantics(), APFloat::rmNearestTiesToEven, &ignored);
return bitwiseIsEqual(Tmp);
}
unsigned int convertToHexString(char *DST, unsigned int HexDigits,
bool UpperCase, roundingMode RM) const {
APFLOAT_DISPATCH_ON_SEMANTICS(
convertToHexString(DST, HexDigits, UpperCase, RM));
}
bool isZero() const { return getCategory() == fcZero; }
bool isInfinity() const { return getCategory() == fcInfinity; }
bool isNaN() const { return getCategory() == fcNaN; }
bool isNegative() const { return getIEEE().isNegative(); }
bool isDenormal() const { APFLOAT_DISPATCH_ON_SEMANTICS(isDenormal()); }
bool isSignaling() const { return getIEEE().isSignaling(); }
bool isNormal() const { return !isDenormal() && isFiniteNonZero(); }
bool isFinite() const { return !isNaN() && !isInfinity(); }
fltCategory getCategory() const { return getIEEE().getCategory(); }
const fltSemantics &getSemantics() const { return *U.semantics; }
bool isNonZero() const { return !isZero(); }
bool isFiniteNonZero() const { return isFinite() && !isZero(); }
bool isPosZero() const { return isZero() && !isNegative(); }
bool isNegZero() const { return isZero() && isNegative(); }
bool isSmallest() const { APFLOAT_DISPATCH_ON_SEMANTICS(isSmallest()); }
bool isLargest() const { APFLOAT_DISPATCH_ON_SEMANTICS(isLargest()); }
bool isInteger() const { APFLOAT_DISPATCH_ON_SEMANTICS(isInteger()); }
APFloat &operator=(const APFloat &RHS) = default;
APFloat &operator=(APFloat &&RHS) = default;
void toString(SmallVectorImpl<char> &Str, unsigned FormatPrecision = 0,
unsigned FormatMaxPadding = 3, bool TruncateZero = true) const {
APFLOAT_DISPATCH_ON_SEMANTICS(
toString(Str, FormatPrecision, FormatMaxPadding, TruncateZero));
}
void print(raw_ostream &) const;
void dump() const;
bool getExactInverse(APFloat *inv) const {
APFLOAT_DISPATCH_ON_SEMANTICS(getExactInverse(inv));
}
friend hash_code hash_value(const APFloat &Arg);
friend int ilogb(const APFloat &Arg) { return ilogb(Arg.getIEEE()); }
friend APFloat scalbn(APFloat X, int Exp, roundingMode RM);
friend APFloat frexp(const APFloat &X, int &Exp, roundingMode RM);
friend IEEEFloat;
friend DoubleAPFloat;
};
/// See friend declarations above.
///
/// These additional declarations are required in order to compile LLVM with IBM
/// xlC compiler.
hash_code hash_value(const APFloat &Arg);
inline APFloat scalbn(APFloat X, int Exp, APFloat::roundingMode RM) {
if (APFloat::usesLayout<detail::IEEEFloat>(X.getSemantics()))
return APFloat(scalbn(X.U.IEEE, Exp, RM), X.getSemantics());
if (APFloat::usesLayout<detail::DoubleAPFloat>(X.getSemantics()))
return APFloat(scalbn(X.U.Double, Exp, RM), X.getSemantics());
llvm_unreachable("Unexpected semantics");
}
/// Equivalent of C standard library function.
///
/// While the C standard says Exp is an unspecified value for infinity and nan,
/// this returns INT_MAX for infinities, and INT_MIN for NaNs.
inline APFloat frexp(const APFloat &X, int &Exp, APFloat::roundingMode RM) {
if (APFloat::usesLayout<detail::IEEEFloat>(X.getSemantics()))
return APFloat(frexp(X.U.IEEE, Exp, RM), X.getSemantics());
if (APFloat::usesLayout<detail::DoubleAPFloat>(X.getSemantics()))
return APFloat(frexp(X.U.Double, Exp, RM), X.getSemantics());
llvm_unreachable("Unexpected semantics");
}
/// Returns the absolute value of the argument.
inline APFloat abs(APFloat X) {
X.clearSign();
return X;
}
/// Returns the negated value of the argument.
inline APFloat neg(APFloat X) {
X.changeSign();
return X;
}
/// Implements IEEE minNum semantics. Returns the smaller of the 2 arguments if
/// both are not NaN. If either argument is a NaN, returns the other argument.
LLVM_READONLY
inline APFloat minnum(const APFloat &A, const APFloat &B) {
if (A.isNaN())
return B;
if (B.isNaN())
return A;
return (B.compare(A) == APFloat::cmpLessThan) ? B : A;
}
/// Implements IEEE maxNum semantics. Returns the larger of the 2 arguments if
/// both are not NaN. If either argument is a NaN, returns the other argument.
LLVM_READONLY
inline APFloat maxnum(const APFloat &A, const APFloat &B) {
if (A.isNaN())
return B;
if (B.isNaN())
return A;
return (A.compare(B) == APFloat::cmpLessThan) ? B : A;
}
/// Implements IEEE 754-2018 minimum semantics. Returns the smaller of 2
/// arguments, propagating NaNs and treating -0 as less than +0.
LLVM_READONLY
inline APFloat minimum(const APFloat &A, const APFloat &B) {
if (A.isNaN())
return A;
if (B.isNaN())
return B;
if (A.isZero() && B.isZero() && (A.isNegative() != B.isNegative()))
return A.isNegative() ? A : B;
return (B.compare(A) == APFloat::cmpLessThan) ? B : A;
}
/// Implements IEEE 754-2018 maximum semantics. Returns the larger of 2
/// arguments, propagating NaNs and treating -0 as less than +0.
LLVM_READONLY
inline APFloat maximum(const APFloat &A, const APFloat &B) {
if (A.isNaN())
return A;
if (B.isNaN())
return B;
if (A.isZero() && B.isZero() && (A.isNegative() != B.isNegative()))
return A.isNegative() ? B : A;
return (A.compare(B) == APFloat::cmpLessThan) ? B : A;
}
} // namespace llvm
#undef APFLOAT_DISPATCH_ON_SEMANTICS
#endif // LLVM_ADT_APFLOAT_H